1,2

Table of n, a(n) for n=1..21.

a(n) = a(n-1) + sum_{1<=i<j<n} (a(j)-a(i))

a(n) = (n+1)(a(n-1)-a(n-2)) + a(n-3) for n>=5.

Conjecture: a(n) = c n! (1+2/n+(5/2)/n^2+(31/6)/n^3+(317/24)/n^4+O(1/n^5)), where c is about 0.1289432494744. - Dean Hickerson, Nov 15 2003

In closed form, c = BesselJ[3,2] = 0.128943249474402051... - Vaclav Kotesovec, Nov 19 2012

26 follows 7 as the sum of the differences of previous terms is (2-1) + (3-1) + (7-1) + (3-2) + (7-2) + (7-3) = 19 and 7+19 = 26.

a[1]=1; a[2]=2; a[3]=3; a[4]=7; a[n_] := a[n]=(n+1)(a[n-1]-a[n-2])+a[n-3]

Sequence in context: A342155 A308114 A092983 * A107881 A128001 A264829

Adjacent sequences: A089705 A089706 A089707 * A089709 A089710 A089711

nonn

Amarnath Murthy, Nov 14 2003

Edited by Dean Hickerson and Ray Chandler, Nov 15 2003

approved